The Roku Box
The Roku Box has many apps, for example Hulu Plus, Netflix, BYU TV, etc. My favorite thing about the Roku is instant streaming channels like Amazon Prime. For families, Amazon Prime is the best thing ever. You get free shipping on your shopping (including Christmas presents) and you get unlimited instant shows. And the cost is a lot cheaper than Netflix. Plus if you own a Kindle Fire, your Amazon Prime shows will work on that as well.
The Apple TV has many features including movies and music. This allows you to easily watch the things you purchase through itunes without the hassle of a dvd (and my little brother has scratched a lot of dvds). That also means you can get movies without going all the way out to the store.
So what is the best one to buy--the XBOX 360. It can do almost everything that the Roku can do and it has the media center. You can browse movies and music. You can purchase arcade games as well as traditional video games. It also plays dvds (but not BluRay).